Is the answer also imaginary?

Algebra Level 4

If \(\omega\) is one of the imaginary cube roots of unity,evaluate\[ \left | \begin{array}{cccc} 1 & \omega & \omega^2 & \omega^3 \\ \omega & \omega^2 & \omega^3 & 1 \\ \omega^2 & \omega^3 & 1 & \omega \\ \omega^3 & 1 & \omega & \omega^2 \end{array} \right |^{2}. \] If the value of above determinant is in the form \(a+b\sqrt{-1}\), find \(a+b\).

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